Analysis of a Simple Recruiting Method for Cooperative Routes and Strip Networks

13 Pages·2010·0.65 MB·English

Analysis of a Simple Recruiting Method for 1
Cooperative Routes and Strip Networks
Aravind Kailas and Mary Ann Ingram
Abstract
The Opportunistic Large Array (OLA) is the basis for a simple cooperative transmission protocol
that is suitable for broadcasting in wireless sensor networks and in which every node transmits once
per broadcast. OLA with Transmission Threshold (OLA-T) is an energy-efficient extension of the OLA
protocol that limits node participation during broadcasting. Performance of OLA-T has been studied
for disc-shaped networks. In this paper, we propose a method to systematically set the transmission
threshold and design the OLAs for two-dimensional strip-shaped networks. Theoretical bounds and
conditions for achieving sustained OLA propagation and reducing the total energy consumption in the
network using OLA-T have been derived in this paper. These results would also apply to arbitrarily
shaped networks that have node participation limited to strip-shaped collections.
I. INTRODUCTION
Cooperative Transmission (CT)-based strategies enable collections of single-antenna radios to
achieve the spatial diversity benefits of an array transmitter, and can be used to save energy and
achieve range-extension [1], [2]. The proposed method is based on a simple form of cooperative
transmission called the Opportunistic Large Array (OLA) [3], which applies to high-density
wireless sensor networks (WSNs). While price is still a barrier to high-density WSNs, continued
development in ultra-low power and energy harvesting radios could someday enable large, dense
multi-hop networks [4]. Such networks might be deployed on structures that are strip-shaped,
TheauthorsgratefullyacknowledgesupportforthisresearchfromtheNationalScienceFoundationundergrantCNS-0721296.
Dr.Mary AnnIngram andAravindKailas arewith theSchool ofElectricaland ComputerEngineering,Georgia Instituteof
Technology, Altanta, GA 30332-0250, USA
for example, dense distributions of wireless strain gages may be deployed on bridges in the
structural health monitoring application [5]. Alternatively, a strip may occur as a “cooperative
route,” within a larger, dense multi-hop network. A cooperative route is a set of nodes that
are candidates for cooperation between a source and a destination; the set is many hops long
and multiple nodes wide, and may be constructed based on a conventional multi-hop route [6],
or by using other means, such as the OLACRA [7] and OLA-ROAD [8] protocols, which do
not require an existing conventional route. This paper assumes that the strip-shaped candidate
set already exists, and provides a simple and systematic way for the cooperators along such
routes to be selected. “Basic OLA” for the strip network was studied in [9]. This paper extends
that work to include a user-defined transmission threshold, which is a mechanism to limit node
participation and save energy.
An OLA is a group of single-antenna relays or forwarding nodes that operate without any
mutual coordination, but naturally fire transmit diversity waveforms in independently fading
orthogonal channels approximately simultaneously in response to energy received from a single
source or another OLA [3]. OLA transmission time synchronization with the root mean square
transmit time delay spreads less than 100 ns have been demonstrated [10]. One simple, power
amplifier-friendly way to achieve transmit diversity is to transmit On-Off-Shift Keying (OOK)
or Frequency-Shift Keying (FSK) on orthogonal carriers, with a simple energy detectors in the
receiver [10]. Even though many nodes may participate in an OLA transmission with diversity,
total transmission energy can still be saved because all nodes can reduce their transmit powers
dramatically and large fade margins are not needed.
When using “Basic OLA” for broadcasting in a network, the nodes repeat if they haven’t
repeated the packet before, and the OLAs will “propagate,” eventually including all the nodes
in the network, under a condition on relay power and receiver sensitivity [3]. In [3], Basic OLA
was shown to yield an energy savings of about 5 dB compared to a popular broadcast tree
algorithm, the Broadcast Incremental Power (BIP) algorithm [11]. OLA-T is the same as Basic
OLA except each node applies a Signal-to-Noise Ratio (SNR) threshold to limit the relaying
nodes to those at the edge of the decoding range [12], [13]. Even though these “border nodes”
must transmit at a higher power than for Basic OLA to sustain propagation [13], total transmit
energy is still saved because in Basic OLA, nodes that are not at the border must waste some
2
transmission energy just getting their signals over other nodes that have already received the
signal.
OLA-T is distinct from cooperative medium access control (MAC) protocols that use SNR
as a basis for relay participation [14]–[17]. In most proposed CT MAC protocols, potential
relays must (i) learn the quality of their links to the destination via feedback [14]–[16], and
(ii) contend for the channel, using, for example, a priority-based contention window size to
favor the preferred relays [14]. In contrast, OLA-T is a purely feed-forward approach (there
is no pre-determined destination for each intermediate OLA-T hop) and there is no contention
among relays, because in any particular hop, the relays transmit synchronously. The paper by
[17] uses an SNR threshold on only the source-relay signal. However, [17] assumes no decoding
error detection at the relay (e.g. CRC check) and requires that a relays SNR must be higher
than the threshold, while the present paper does the opposite on both points; furthermore [17]
analyzes the error probability of a single link whereas this paper analyzes the requirements for
successful transmission over an unlimited number of hops.
II. SYSTEM MODEL
For our analysis, we adopt the notation and assumptions of [13], some of which were used
earlier in [9]. Half-duplex nodes are assumed to be distributed randomly and uniformly over a
continuous strip defined by S = {(x,y) : |y| ≤ W, 0 ≤ x ≤ L} with average node density ρ,
2
width W, and length L.
We assume a node can decode and forward (DF) a packet without error when its received
signal-to-noise ratio (SNR) is greater than or equal to a modulation-dependent ‘lower’ threshold,
τ [13]. In practice, there is no explicit SNR threshold; nodes DF only if they pass CRC check. In
l
contrast, the ‘Transmission’ or ‘upper’ threshold, τ is used explicitly in the receiver to compare
u
against the received SNR. This additional criterion for relaying limits the number of nodes in
each hop because a node would relay only if its received SNR is less than τ . Assumption of
u
unit noise variance transform τ and τ to received powers, which define a range of received
l u
powers that correspond to the “significant” boundary nodes, which form the OLA. We define
the Relative Transmission Threshold (RTT) as R = τu.
τ
l
For simplicity, the deterministic model [9] is assumed, which means that the power received
3
at a node is the sum of the powers from each of the node transmissions. This implies that
signals received from different nodes are orthogonal. Techniques to induce orthogonality in the
node transmissions by randomly delaying the firing times (such as in [18]) or transmitting on
orthogonal carriers (Frequency Division Multiplexing) will work as long as the receivers can
extract the multipath diversity from the wireless channel.
Following the Continuum Model for a strip network from [9], we assume a non-fading
environment and a path-loss exponent of 2. The path-loss function in Cartesian coordinates
is given by l(x,y) = (x2 +y2)−1, where (x,y) are the normalized coordinates at the receiver.
As in [13], distance d is normalized by a reference distance, d . Let the normalized source and
0
relay transmit powers be denoted by P and P , respectively, and the relay transmit power per
s r
unit area be denoted by P = ρP . The normalization is such that P and P are actually the
r r s r
SNRs at a receiver d away from the transmitter [13]. Since we assume a continuum of nodes
0
in the network, we let the node density ρ become very large (ρ → ∞) while P is kept fixed.
r
Our results are parameterized by R and node degree, K, which for any finite node density, can
be expressed as K = πP /τ [7]. Columns 2–6 of Table I give some example values of our key
r l
parameters.
III. OLA-T FOR THE STRIP NETWORK
In this section, the analytical framework for deriving the necessary and sufficient conditions
for sustained broadcast using OLA-T is developed. Fig. 1 represents the propagation of a packet
along a strip network using OLA with Transmission Threshold (OLA-T). The source node,
S, initiates the packet transmission and all the nodes in the vicinity of the source node that
can decode the packet form the first Decoding Level, D . The nodes in D that satisfy the
1 1
transmission threshold constitute the “OLA-1” nodes or the first OLA, and are denoted by S
1
in Fig. 1. Mathematically, S = {(x,y) ∈ S : τ ≤ (cid:82) (cid:82) P l(x,y)dxdy ≤ τ }.
1 l s u
Next, the set of nodes in the vicinity of OLA 1 that decode the packet, but have not previously
decoded the same packet, form the second Decoding Level, D . Again, only the nodes in D
2 2
that satisfy the transmission threshold constitute the “OLA-2” nodes, denoted by S in Fig. 1.
2
(cid:90) (cid:90)
In general, S = {(x,y) ∈ S\(cid:83)k−1D : τ ≤ P l(x−x(cid:48),y−y(cid:48))dx(cid:48)dy(cid:48) ≤ τ } is used to
k i=1 i l r u
S
k−1
define the OLA-k nodes.
4
A. Rectangular Approximation
We assume that the width of the strip, W, the hop distance, r , and the OLA lengths, d ,
o,k k
of the k-th hop, are such that the ‘curved’ decoding ranges (the regions between the solid and
dash-dot lines) S can be approximated by the ‘shaded’ rectangles S˜ shown in Fig. 1. In Table I,
k k
Columns 8–10 correspond to hop index >> 1 or steady state. It can be seen that the straight-line
approximation results in low approximation errors in Examples 1, 2, 3, and 5, while Examples
4 and 5 show that a smaller W yields a better approximation. We also observe that the high
density cases, Examples 1, 2, and 3, correspond to very low transmit powers.
With this approximation, we can derive the boundaries for the k-th OLA for the OLA-T pro-
tocol. The inner and outer boundaries that define the OLA-1 nodes are r and r , respectively,
i,1 o,1
(cid:113)
as shown in Fig. 1. Using the definition of the path-loss functions defined previously, r = Ps
i,1 τu
(cid:113) (cid:113) (cid:113)
and r = Ps. S˜ is the first OLA with boundary conditions given by Ps ≤ x ≤ Ps and
o,1 τl 1 τu τl
(cid:113) (cid:113)
|y| ≤ W. We denote the length of the first OLA as d , given by d = r −r = Ps − Ps.
2 1 1 o,1 i,1 τl τu
In order to approximate the curved inner and outer boundaries for S by straight lines, r
2 i,2
(cid:90) (cid:90)
and r are chosen to satisfy P l(x−[r +d +r ],y)dxdy = τ , where Γ = u when
o,2 r i,1 1 Ω,2 Γ
S˜
1
Ω = i and Γ = l when Ω = o. We observe from the previous equation, and Fig. 1, that r and
i,2
r are both defined relative to r . By substituting the definition for l(x,y) and making the
o,2 o,1
(cid:90) W/2 (cid:90) ro,2+d1 P (cid:90) ro,2+d1 2P (cid:18)W(cid:19)
r r
limits explicit, we can write, dxdy = arctan dx = τ .
x2 +y2 x 2x l
(cid:18) −(cid:19)W/2 ro,2 ro,2
Similarly,(cid:82)ri,2+d1 2Prarctan W dx = τ .So,S˜ isthesecondOLAwithalengthd = r −r .
ri,2 x 2x u 2 2 o,2 i,2
In this way, the subsequent OLA lengths d ,d ,... can be found iteratively d = r −r =
3 4 k o,k i,k
h (d ) − h (d ), where the functions h (d ) for d > 0, Ω ∈ {i,o} are defined as
o k−1 i k−1 Ω k−1 k−1
(cid:90) hΩ(dk−1)+dk−1 2P (cid:18)W(cid:19)
r
the unique solutions of arctan du = τ , where Γ = u when Ω = i and
Γ
u 2u
hΩ(dk−1)
Γ = l when Ω = o. We denote h (·)−h (·) = g(·). So, d = g(d ). The following properties
o i k+1 k
for g(·) have been proved in the Appendix.
1) limg(d) = 0.
d→0
2) The function g is monotonically increasing.
3) The function g is concave downward.
4) The tangent at zero, g(cid:48)(0), is given by g(cid:48)(0) = h(cid:48)(0)−h(cid:48)(0) = 1 − 1 .
o i exp(1)−1 exp(R)−1
K K
5) When g(cid:48)(0) > 1, then g has a unique positive fixed point g(d) = d. When g(cid:48)(0) < 1, the
5
only fixed point of g is at d = 0.
B. Sufficient and Necessary Conditions for Infinite OLA Propagation
(cid:88)
Infinite propagation of the packet is determined by how the sum d grows with k. When
k
k
this sum is unbounded, the OLAs (and hence, the packet) will propagate forever keeping the
link between the source and destination intact irrespective of the distance between these points.
However, if the sum is finite, then the packet does not reach the destination when the source
and destination are too far apart.
The propagation of the packet along the strip network can be predicted by computing the slope
of the concave function g at zero [9]. In particular, Properties (4) and (5) of g(·) imply analytical
expressions for the two extreme cases: Transmissions reach a steady state when g(cid:48)(0) > 1 and
(cid:0) (cid:1)
die out when g(cid:48)(0) < 1. Equivalently, transmissions reach a steady state when 2 > exp 1 +
K
(cid:0) (cid:1) (cid:0) (cid:1)
exp −R .WeobservethatwhenR → ∞,exp −R/K → 0,OLA-TbecomesBasicOLA,and
K
the above equations become the conditions in [9]. Finally, the condition for sustained propagation
(cid:20) (cid:21)
(cid:0) (cid:1)
can be re-written in terms of a lower bound for R: R = −Kln 2 − exp 1 . So,
lowerbound K
R < R results in very thin OLAs (fewer nodes) that are too weak to sustain infinite
lowerbound
propagation and eventually die out. We observe that this is the same lower bound as for the
infinite disc network in [13]. We note that a similar condition held for both the disc and strip
networks using Basic OLA [3], [9].
IV. NUMERICAL RESULTS AND DISCUSSION
Fig. 2 shows the lower bound on RTT, R , in dB, versus the node degree, K. It is
lowerbound
observedthatasK increases,theminimum sizeofthe‘SNRwindow’decreases. Forexample,for
K = 1, the minimum transmission threshold is about 1.8 dB higher than the decoding threshold.
While for K = 10, the minimum transmission threshold is only 0.2 dB higher than the decoding
threshold. It can also be inferred that theoretically, it is possible for OLA-T to achieve infinite
network broadcast with an infinitesimally small R and very high K. However, a very
lowerbound
small R may not be very effective if there is too much uncertainty in the SNR or if the
lowerbound
node density is not high enough.
6
Fig. 3 shows the two extreme cases of g(cid:48)(x), depending on the value of the slope at x = 0. To
generate these results, a node degree, K = π was assumed, which resulted in R = 1.476
lowerbound
or 1.68 dB. Violation of the lower bound should correspond to g(cid:48)(0) < 1. To check this, R was
chosen to be 1.3 (1.13 dB) and 3 (4.77 dB), for the cases, g(cid:48)(0) < 1 and g(cid:48)(0) > 1, respectively.
g(cid:48)(0) < 1 ⇒ R < R case is denoted by the dotted curve in Fig. 3. The other extreme is
lowerbound
when g(cid:48)(0) > 1 ⇒ R > R , and this is represented by the dash-circle curve in Fig. 3. A
lowerbound
fixed-point attractor away from zero at about x = 2 can be observed for the dash-circle curve,
ensuring that the transmissions don’t die out.
A. Energy Evaluation of OLA-T
We use the fraction of radiated energy saved (FES) as the metric for comparing the energy-
efficiency of OLA-T relative to Basic OLA. Under the continuum assumption, the total energy
consumption is simply the area of the rectangular OLAs. The FES for the strip network is
computed as follows. The radiated energy consumed by OLA-T in the first N levels is mathe-
N
(cid:88)
matically expressed as E = P T W d , where P is the lowest value of P that
rad(OT) r(OT) s k r(OT) r
k=1
would guarantee successful broadcast using OLA-T and T is the length of the packet in time
s
N
(cid:88)
units. The energy consumed by Basic OLA is E = P T Wr , where r = r ,
rad(O) r(O) s strip strip o,k
k=1
and P is the lowest value of P that would guarantee successful broadcast using Basic OLA.
r(O) r
N
(cid:88)
So, FES can be expressed as: FES = 1−(E /E ) = 1−(K ln2 d /r ), where
rad(OT) rad(O) (OT) k strip
k=1
K is the node degree for OLA-T to guarantee successful broadcast when operating in its
(OT)
minimum power configuration.
In wireless sensor networks, the radiated energy does not always dominate the total energy
budget. Let the total circuit-consumed energy (E ) consumed by the network be proportional to
cir
E : E = αE . Then, we can define the whole-energy fraction of energy saved (WFES)
rad(O) cir rad(O)
(cid:18) (cid:19) (cid:18) (cid:19)(cid:18) (cid:19)
as follows: WFES = 1 − Erad(OT)+Ecir = 1 1 − Erad(OT) = FES. For example, if the
Erad(O)+Ecir 1+α Erad(O) 1+α
circuit-consumed energy in a relaying node is the same as its radiated energy, then α = 1. When
α = 0, we only consider the radiated energy (i.e., WFES = FES), and when α (cid:54)= 0, the circuit
energy is some fraction of the radiated energy. Even though no hardware-defined radios exist
today that can support OLA transmissions, we can still consider some existing radio profiles.
7
For example, for the XE1205, we have α ≈ 0.22, and for the nRF905, we have α ≈ 0.4 [20].
Fig. 4 shows WFES versus node degree, K (on a logarithmic scale), for a strip network
(OT)
for different values of α and N = 30. For example, for α = 0, at K = 10, FES is about 0.55.
(OT)
This means that at their respective lowest energy levels at K = 10, OLA-T saves about 55%
(OT)
of the radiated energy used by Basic OLA. On the other hand, when both the circuit and transmit
energies are equal or α = 1, and K = 10, the WFES is about 0.28, meaning that OLA-T
(OT)
saves about 28% of the total energy consumed during broadcast relative to Basic OLA, both
protocols operating in their minimum power configurations. It is noted that WFES increases with
K and attains a maximum of about 62%. This is because high values of K imply fewer
(OT) (OT)
nodes in every hop (i.e. very slender OLA strips), which reduces the overall energy consumption
in the network during broadcast.
B. OLA-T for a Disc Compared to the Strip
Interestingly, the WFES in a strip network is almost twice that of the WFES for a disc network
from [13]. Intuitively, the reason is that the OLA part of the Decoding Level 1 is a significantly
larger portion of the whole for the disc compared to the strip. The analytical reasoning for this is
presented below. Consider the WFES for just the first OLA for both networks, because the first
level dominates in the comparison. Let r and r be the inner and outer boundaries for the first
i,1 o,1
OLA, respectively, and let d = r −r . We note that the values of these parameters are equal
1 o,1 i,1
(cid:18) (cid:19)(cid:18) (cid:19)
for disc and strip networks (see Section III.A). WFES = 1− d1 1 , and WFES =
strip ro,1 1+α disc
(cid:18) (cid:19)(cid:18) (cid:19) (cid:18) (cid:19)(cid:18) (cid:19)
1− ro2,1−ri2,1 1 . Observe that WFES = 1− d1 (ro,1 +ri,1) 1 < WFES .
ro2,1 1+α disc ro,1 ro,1 1+α strip
(cid:124) (cid:123)(cid:122) (cid:125)
>1
V. CONCLUSIONS
In this paper, we analyzed a simple form of a cooperative transmission protocol, the Op-
portunistic Large Array with Transmission Threshold (OLA-T), for broadcasting along a strip
network. It was shown that as long as the transmission threshold is above a critical value, the
packet is delivered to the destination regardless of the distance between the source and the
destination. The OLA-T protocol limits the node participation in a strip and was found to save
as much as 62% of the transmitted energy relative to Basic OLA, when both protocols operated
8
in their lowest power configurations. Future work includes a detailed analysis of the protocol
for different path-loss exponents and finite node density.
APPENDIX
The properties listed in Section III–a are proved below, using the same list indices.
1) In [9], it was shown that limh (x) = 0, Ω ∈ {i,o}. Since, g(x) = h (x) − h (x), it
Ω o i
x→0
follows that lim(h (x)−h (x)) = limg(x) = 0.
o i
x→0 x→0
2) In order to show g(cid:48)(·) > 0, we differentiate with respect to x, to get g(cid:48)(x) = h(cid:48)(x)−h(cid:48)(x).
o i
From [9], we know that h(cid:48) (x) = U(hΩ(x)+x) , where Ω = {i,o} and U(x) =
(cid:18) (cid:19) Ω U(hΩ(x))−U(hΩ(x)+x)
1arctan 1 . Since U(·) is a decreasing function for x > 0, we also know that h (x)
x 2x o
and h (x) are increasing functions in x. We use h and h instead of h (x) and h (x),
i o i o i
respectively, for the sake of brevity. Further simplification results in the following closed-
form expression for g(cid:48)(x): g(cid:48)(x) = U(hi)U(ho+x)−U(ho)U(hi+x) . The denominator is a
[U(ho)−U(ho+x)]·[U(hi)−U(hi+x)]
product of positive terms, and so in order to complete the proof, it suffices to show that
U(h )U(h +x)−U(h )U(h +x) > 0 ⇒ U(hi) > U(ho) . In other words, we need to
i o o i U(hi+x) U(ho+x)
show that q(h,x) := U(h) is decreasing in ‘h’. However, because h and h are difficult
U(h+x) i o
to obtain, we computed them using iterative numerical methods. Thus, U(h ), U(h ),
i o
U(hi) , and U(ho) are also computed numerically, upon which it can be verified that
U(hi+x) U(ho+x)
q(h,x) is decreasing in h ∀x > 0. So, the inequality holds proving that g is a monotonically
increasing function.
3) Numerically, it is found that h (x) and h (x) are concave downward functions, ie., h(cid:48)(cid:48)(x) <
o i (cid:34) o (cid:35)
U2(h +x)U2(h ) U(cid:48)(h +x) U(cid:48)(h )
0 and h(cid:48)(cid:48)(x) < 0. From [9], h(cid:48)(cid:48)(x) = Ω Ω · Ω − Ω ,
i Ω [U(h )−U(h +x)]3 U2(h +x) U2(h )
Ω Ω Ω Ω
(cid:124) (cid:123)(cid:122) (cid:125)
(cid:124) (cid:123)(cid:122) (cid:125)
=:v(hΩ,x) =:w(hΩ,x)
where Γ = u when Ω = i and Γ = l when Ω = o. Since closed-form expressions for h
i
and h are very difficult to obtain, v(h,x) and w(h,x) were computed numerically. It can
o
be verified that the product v(h,x)·w(h,x) is decreasing in h, i.e., v(h ,x)·w(h ,x) >
i i
v(h ,x)·w(h ,x) ∀x > 0. Thus, g(cid:48)(cid:48)(·) < 0, implying that g is concave downward.
o o
4) Using the results from [9], h(cid:48)(0) = 1 and h(cid:48)(0) = 1 . Since g(cid:48)(0) = h(cid:48)(0)−
o exp(1)−1 i exp(R)−1 o
K K
h(cid:48)(0), (5) follows.
i
9
5) We know that g(cid:48)(x) = h(cid:48)(x) − h(cid:48)(x). Since h(cid:48) (x) −x−→−∞→ 0, Ω ∈ {o,i}, it follows that
o i Ω
g(cid:48)(x) → 0 as x → ∞. If g(cid:48)(0) > 1, then g(x) > x for all x > 0 small enough. Since,
g(·) is increasing and g(cid:48)(x) → 0, g(x) < x, for x large enough, i.e. the local attractor
is away from the origin. On the other hand, when g(cid:48)(0) < 1, g(x) < x for sufficiently
small x > 0. From the concavity of g, it follows that g(x) = x can happen only at x = 0,
i.e. the local attractor is the origin. Finally, in [9], the existence and uniqueness of h (·)
Ω
for Ω ∈ {o,i} was proved. Using the property that g(·) is monotonically increasing, it
follows that for x (cid:54)= x , g(x ) (cid:54)= g(x ), i.e., the solutions to g(·) are unique, and when
1 2 1 2
x (cid:54)= x , g(x ) = g(x ), it just implies that the OLA propagation continues with fixed step
1 2 1 2
sizes after the initial transient phase.
REFERENCES
[1] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation – Part I: System description, Part II: Implmentation aspects
and performance analysis,” IEEE Trans. Commun., vol. 51, no. 11, pp. 1927–48, Nov. 2003.
[2] J. N. Laneman, D. Tse, and G. W. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage
behaviour,”IEEE Trans. Inf. Theory, vol. 50, no. 12, pp. 3063–3080, Dec. 2004.
[3] Y. W. Hong and A. Scaglione, “Energy-efficient broadcasting with cooperative transmissions in wireless sensor networks,”
IEEE Trans. Wireless Commun., vol. 5, no. 10, pp. 2844–55, Oct. 2006.
[4] V. Raghunathan, C. Schurgers, S. Park, and M. Srivastava, “Energy aware wireless microsensor networks,” IEEE Signal
Process. Mag., vol. 19, no. 2, pp. 40–50, Mar. 2002.
[5] Y.ZhangandJ.Li,“Wavelet-basedsensordatacompressiontechniqueforcivilinfrastructureconditionmonitoring,”ASCE
J. of Comput. Civil Engr., vol. 20, no. 6, pp. 390–399.
[6] S. Savazzi and U. Spagnolini, “Energy aware power allocation strategies for multi-hop-cooperative transmission schemes,”
IEEE J. Sel. Areas Commun., vol. 25, no. 2, pp. 318–327, Feb. 2007.
[7] L.Thanayankizil,A.Kailas,andM.A.Ingram,“Routingprotocolsforwirelesssensornetworksthathaveanopportunistic
large array (OLA) physical layer,” Ad-Hoc & Sensor Wireless Networks, vol. 8, pp. 79–117, 2009.
[8] L. Thanayankizil and M. A. Ingram, “Reactive robust routing with opportunistic large arrays,” Proc.IEEE International
Communication Conference (ICC) Workshop, June 2009.
[9] B. Sirkeci-Mergen and A. Scaglione,“A continuum approach to dense wireless networks with cooperation,” Proc. IEEE
Conference on Computer Communications (INFOCOM), Vol. 4, pp. 2755–63, 2005.
[10] Y.J.Chang,M.A.Ingram,andR.S.Frazier,“Clustertransmissiontimesynchronizationforcooperativetransmissionusing
software defined radio,” CoCoNet Workshop, IEEE International Communication Conference (ICC), accepted, May 2010.
[11] J. Wieselthier, G. Nguyen, and A. Ephremides, “On the construction of energy-efficient broadcast and multicast trees in
wireless networks,” Proc. IEEE Conference on Computer Communications (INFOCOM), Mar. 2000, pp. 585–594.
[12] B.Sirkeci-MergenandA.Scaglione,“Onthepowerefficiencyofcooperativebroadcastindensewirelessnetworks,”IEEE
J. Sel. Areas Commun., vol. 25, no. 2, pp. 497–507, Feb. 2007.
10